On Liouville's theorem for the Hessian quotient equation $\sigma_2/\sigma_1$
Analysis of PDEs
2026-02-17 v1
Abstract
We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation in . The proof is based on the observation that after rewriting the quotient operator as the operator, acting on a new function, one can refer to the recent result of Shankar and Yuan on Liouville's theorem for equation.
Keywords
Cite
@article{arxiv.2602.14946,
title = {On Liouville's theorem for the Hessian quotient equation $\sigma_2/\sigma_1$},
author = {Siyuan Lu and Marcin Sroka},
journal= {arXiv preprint arXiv:2602.14946},
year = {2026}
}